Question: Solve for $x$ and $y$ using elimination. ${-6x+6y = -30}$ ${5x+5y = 55}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $6$ ${-30x+30y = -150}$ $30x+30y = 330$ Add the top and bottom equations together. $60y = 180$ $\dfrac{60y}{{60}} = \dfrac{180}{{60}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {-6x+6y = -30}\thinspace$ to find $x$ ${-6x + 6}{(3)}{= -30}$ $-6x+18 = -30$ $-6x+18{-18} = -30{-18}$ $-6x = -48$ $\dfrac{-6x}{{-6}} = \dfrac{-48}{{-6}}$ ${x = 8}$ You can also plug ${y = 3}$ into $\thinspace {5x+5y = 55}\thinspace$ and get the same answer for $x$ : ${5x + 5}{(3)}{= 55}$ ${x = 8}$